论文标题
嵌入第三部分上的遥远的2色组件：一般情况
Distant 2-Colored Components on Embeddings Part III: The General Case
论文作者
论文摘要
这是三篇论文中的第三篇，我们证明了托马森（Thomassen）的5-毫无用处定理的以下概括：让$ g $是嵌入在$ g $属表面上的有限图。然后$ g $可以是$ l $颜色的，其中$ l $是$ g $的列表分配，其中每个顶点都有5个列表，除了一系列成对的远距离组件集合，每个顶点都有普通的2彩色的精确度，只要$ g $的面部宽度至少是至少$ 2^{g）$ 2^{ω$ 2^{Ω $ 2^{ω（g）} $。这为Thomassen的猜想的广义版本提供了肯定的答案，并概括了2017年DvoDimák，Lidický，Mohar和Tostle of Tostaint the Extant Pregant的顶点。在上一篇论文中，我们证明了上述结果适用于没有长度为三个或四个的分离循环的限制类别的嵌入类别。在本文中，我们使用此特殊情况来证明结果在一般情况下存在。
This is the third in a sequence of three papers in which we prove the following generalization of Thomassen's 5-choosability theorem: Let $G$ be a finite graph embedded on a surface of genus $g$. Then $G$ can be $L$-colored, where $L$ is a list-assignment for $G$ in which every vertex has a 5-list except for a collection of pairwise far-apart components, each precolored with an ordinary 2-coloring, as long as the face-width of $G$ is at least $2^{Ω(g)}$ and the precolored components are of distance at least $2^{Ω(g)}$ apart. This provides an affirmative answer to a generalized version of a conjecture of Thomassen and also generalizes a result from 2017 of Dvořák, Lidický, Mohar, and Postle about distant precolored vertices. In a previous paper, we proved that the above result holds for a restricted class of embeddings which have no separating cycles of length three or four. In this paper, we use this special case to prove that the result holds in the general case.
